Do not caulk there. It will be an ugly mess. Add quarter-round.

sanded and refinished. After it was done, we found that the hardwood
floor now has a "gap" at the edges of the floor and the wall (probably
drywall, not sure what is the material). I'm thinking of doing some

How big a gap, and where does it go? If it's a big enough gap,
and it leads to an air-space, or down through the subfloor, or anywhere
else it's likely to be a entrypoint for drafts of vermin, then you might
stuff it with weatherstripping and THEN cover it with molding.

--Goedjn